Fair Infinite Lotteries, Qualitative Probability, and Regularity

Abstract

A number of philosophers have thought that fair lotteries over countably infinite sets of outcomes are conceptually incoherent by virtue of violating Countable Additivity. In this paper, I show that a qualitative analogue of this argument generalizes to an argument against the conceptual coherence of a much wider class of fair infinite lotteries—including continuous uniform distributions. I argue that this result suggests that fair lotteries over countably infinite sets of outcomes are no more conceptually problematic than continuous uniform distributions. Along the way, I provide a novel argument for a weak qualitative, epistemic version of Regularity.

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